Which line is parallel to the line y=−2x−4

Question

and goes through the point (2, 1)
?(1 point)
Responses

y=−2x+5
y is equal to negative 2 x plus 5

y=−1/2x+5
y is equal to negative 1 half x plus 5

y=−2x−4
y is equal to negative 2 x minus 4

y=1/2x
y is equal to 1 half x

Answer 1

To find a line that is parallel to the line \( y = -2x - 4 \) and goes through the point \( (2, 1) \), we first note that parallel lines have the same slope. The slope of the given line is \(-2\).

Next, we use the point-slope form of the equation of a line, which is

\[ y - y_1 = m(x - x_1) \]

where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Here, \( m = -2 \) and the point is \( (2, 1) \). Substituting these values gives us:

\[ y - 1 = -2(x - 2) \]

Now, simplify this equation:

\[ y - 1 = -2x + 4 \] \[ y = -2x + 5 \]

Thus, the equation of the line that is parallel to \( y = -2x - 4 \) and passes through the point \( (2, 1) \) is:

\[ y = -2x + 5 \]

So the correct response is:

y=−2x+5